Problem: Rewrite as a simplified fraction. ${0.47\overline{5} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 475.5555...\\ 100x &= 47.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 428}$ ${x = \dfrac{428}{900}} $ ${x = \dfrac{107}{225}} $